Summary of the Research done at Salalah College of Technology

MAIN FIELDS OF RESEARCH:Mathematical Optics
I am working towards a unified treatment of light beam optics and polarization,
using the standard mathematical machinery of quantum mechanics. Dirac-like
form of the Maxwell equations is well known in literature. Starting with the
Dirac-like form of the Maxwell’s equations a unified treatment of light
beam optics and polarization has been obtained. The traditional results
(including aberrations) of the scalar optics are modified by the
wavelength-dependent contributions. Some of the well-known results
in polarization studies are realized as the leading-order limit of a
more general framework of our formalism. The existing matrix
representations of the Maxwell’s equations were found to be approximate
for the formalism developed here; hence, an exact matrix representation
of the Maxwell’s equations was derived.

A related study was made starting with the scalar approximation of the
Maxwell’s equations. Using the analogy of the Helmholtz equation with
the Klein-Gordon equation and the Feshbach-Villars approach to the
Klein-Gordon equation a formalism utilizing the powerful techniques of
quantum mechanics has been developed for scalar optics including aberrations.
This provides an alternative to the traditional square-root approach
and gives rise to wavelength-dependent contributions modifying the aberration
coefficients.

Some of the results have been published and others have been communicated.

Quadricmeter is the instrument devised to identify (distinguish) and measure the various
parameters (axis, foci, latera recta, directrix, etc.,) completely characterizing the important
class of surfaces known as the quadratic surfaces. Quadratic surfaces (also known as quadrics)
include a wide range of commonly encountered surfaces including, cone, cylinder, ellipsoid,
elliptic cone, elliptic cylinder, elliptic hyperboloid, elliptic paraboloid, hyperbolic cylinder,
hyperbolic paraboloid, paraboloid, sphere, and spheroid. Quadricmeter is a generalized form of
the conventional spherometer and the lesser known cylindrometer (also known as the “Cylindro-Spherometer”
and "Sphero-Cylindrometer").
With a conventional spherometer it was possible only to measure the radii of spherical surfaces.
Cylindrometer can measure the radii of curvature of a cylindrical surface in addition to the spherical
surface. In both the spherometer and the cylindrometer one assumes the surface to be either spherical
or cylindrical respectively. In the case of the quadricmeter, there are no such assumptions.

* Appeared on the Cover Page.
* The article discusses the cylindrometer (also known as Cylindro-Spherometer and Sphero-Cylindrometer),
fabricated by the author. Cylindrometer (Cylindro-Spherometer and Sphero-Cylindrometer) measures the
radii of curvature of cylindrical surfaces in addition to the spherical surfaces.
View the image:

The set of equivalent resistances formed by any conceivable network
(series/parallel or bridge, or non-planar configurations) of n equal resistors has over twenty
Integer Sequences associated with it. Ten new Integer Sequences occurring in the following
article are listed below:

* Appeared on the Cover Page.
* The article discusses the cylindrometer (also known as Cylindro-Spherometer and Sphero-Cylindrometer),
fabricated by the author. Cylindrometer (Cylindro-Spherometer and Sphero-Cylindrometer) measures the
radii of curvature of cylindrical surfaces in addition to the spherical surfaces.
View the image: